# Hyperboloid of One Sheet

The hyperboloid Of One Sheet is a surface of revolution of the curve family hyperbola.

The parametric formula for the Hyperboloid of One Sheet is:

```ParametricPlot3D[{Cosh[u]*Cos[v], Cosh[u]*Sin[v], Sinh[u]}, {u, -2, 2}, {v, 0, 2*π}]
(* u → height, v → circular sweep. *)```

hyperboloid1.nb.zip

### Ruled Surface

A revolving around its transverse axis forms a surface called “hyperboloid of one sheet”. A hyperboloid is a Ruled Surface.

Ruled surfaces are surfaces that for every point on the surface, there is a line on the surface passing it. Or, in other words, a surface generated by a line. If for each point on the surface there are two lines on the surface passing it, then it's called doubly-ruled surface. Hyperboloid is a doubly-ruled surface.

Ruled surfaces also include cylinder and helicoid. There are only 3 doubly ruled surfaces: The hyperboloid, hyperbolic paraboloid, and plane.

#### Spinning Cube Silhouette

The silhouette of a rotating dice is a hyperbola.